# Definition:Metrizable Topology

## Definition

Let $\struct {S, d}$ be a metric space.

Let $\struct {S, \tau}$ be the topological space induced by $d$.

Then for any topological space which is homeomorphic to such a $\struct {S, \tau}$, it and its topology are defined as metrizable.

## Also see

• Results about metrizable topologies can be found here.

## Linguistic Note

The UK English spelling of metrizable is metrisable, but it is rarely found.